What is log_{b}(7x\times 2y) ?

The solution to log_{b}(7x\times 2y) is log_{b}(14)+log_{b}(x)+log_{b}(y)

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simplify log_{b}(7x\times 2y)

simplify

lo g_{b} (7 x \cdot 2 y)

lo g_{b} (14) + lo g_{b} (x) + lo g_{b} (y)

Solution steps

lo g_{b} (7 x \cdot 2 y)

Simplify

7 x \cdot 2 y : 14 x y

= lo g_{b} (14 x y)

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{b} (14 x y) = lo g_{b} (14) + lo g_{b} (x) + lo g_{b} (y)

= lo g_{b} (14) + lo g_{b} (x) + lo g_{b} (y)

9 lo g_{10} (x) - \frac{1}{3} lo g_{10} (y) - \frac{2}{3} lo g_{10} (z)

lo g_{10} (\frac{x ^{5}}{z})

lo g_{b} (\frac{x ^{2} - 1}{x ^{2} - 4})

lo g_{10} (\frac{4 x ^{3}}{y ^{2} ( x - 1 ) ^{5}})

10 ln (3 x) - [ln (3 x)]^{2}

What is log_{b}(7x\times 2y) ?
The solution to log_{b}(7x\times 2y) is log_{b}(14)+log_{b}(x)+log_{b}(y)